Question
In how many ways can 6 bicycles be parked in a row?
Answers
Answered by
GPT-4o mini
To find the number of ways to park 6 bicycles in a row, we can treat the bicycles as distinct objects since they can be placed in any order.
The number of arrangements of \( n \) distinct objects is given by \( n! \) (read as "n factorial"), which is the product of all positive integers up to \( n \).
For 6 bicycles, we calculate the factorial \( 6! \) as follows:
\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1
\]
Calculating step by step:
\[
6 \times 5 = 30
\]
\[
30 \times 4 = 120
\]
\[
120 \times 3 = 360
\]
\[
360 \times 2 = 720
\]
\[
720 \times 1 = 720
\]
Thus, the total number of ways to park 6 bicycles in a row is \( 720 \).
Therefore, the final answer is:
\[
\boxed{720}
\]
The number of arrangements of \( n \) distinct objects is given by \( n! \) (read as "n factorial"), which is the product of all positive integers up to \( n \).
For 6 bicycles, we calculate the factorial \( 6! \) as follows:
\[
6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1
\]
Calculating step by step:
\[
6 \times 5 = 30
\]
\[
30 \times 4 = 120
\]
\[
120 \times 3 = 360
\]
\[
360 \times 2 = 720
\]
\[
720 \times 1 = 720
\]
Thus, the total number of ways to park 6 bicycles in a row is \( 720 \).
Therefore, the final answer is:
\[
\boxed{720}
\]